Compact Kähler manifolds with partially semi-positive curvature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912946607620096 |
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| author | Zhang, Shiyu Zhang, Xi |
| author_facet | Zhang, Shiyu Zhang, Xi |
| contents | In this paper, we study MRC fibrations of compact Kähler manifolds with partially semi-positive curvature. We first prove that a compact Kähler manifold is rationally connected if its tangent bundle is BC-$p$ positive for all $1\leq p\leq \dim X$. As applications, we confirm a conjecture that any compact Kähler manifold with positive orthogonal Ricci curvature must be rationally connected, and generalize a result of Heier-Wong and Yang to the conformally Kähler case. The second result concern structure theorems for two immediate curvature conditions. We prove that, a compact Kähler manifold with $k$-semi-positive Ricci curvature or semi-positive $k$-scalar curvature, either the rational dimension $\geq n-k+1$ or it admits a locally constant fibration $f: X\rightarrow Y$ such that the fibre is rationally connected and the image $Y$ is Ricci-flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact Kähler manifolds with partially semi-positive curvature Zhang, Shiyu Zhang, Xi Differential Geometry Algebraic Geometry Complex Variables In this paper, we study MRC fibrations of compact Kähler manifolds with partially semi-positive curvature. We first prove that a compact Kähler manifold is rationally connected if its tangent bundle is BC-$p$ positive for all $1\leq p\leq \dim X$. As applications, we confirm a conjecture that any compact Kähler manifold with positive orthogonal Ricci curvature must be rationally connected, and generalize a result of Heier-Wong and Yang to the conformally Kähler case. The second result concern structure theorems for two immediate curvature conditions. We prove that, a compact Kähler manifold with $k$-semi-positive Ricci curvature or semi-positive $k$-scalar curvature, either the rational dimension $\geq n-k+1$ or it admits a locally constant fibration $f: X\rightarrow Y$ such that the fibre is rationally connected and the image $Y$ is Ricci-flat. |
| title | Compact Kähler manifolds with partially semi-positive curvature |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2504.13155 |